Boundary scattering, symmetric spaces and the principal chiral model on the half-line

TY - JOUR

T1 - Boundary scattering, symmetric spaces and the principal chiral model on the half-line

AU - MacKay, N.J.

AU - Short, Ben

PY - 2003/2

Y1 - 2003/2

N2 - We investigate integrable boundary conditions (BCs) for the principal chiral model on the half-line, and rational solutions of the boundary Yang-Baxter equation (BYBE). In each case we find a connection with (type I, Riemannian, globally) symmetric spaces G/H: there is a class of integrable BCs in which the boundary field is restricted to lie in a coset of H; these BCs are parametrized by G/H×G/H; there are rational solutions of the BYBE in the defining representations of all classical G parametrized by G/H; and using these we propose boundary S-matrices for the principal chiral model, parametrized by G/H×G/H, which correspond to our boundary conditions.

AB - We investigate integrable boundary conditions (BCs) for the principal chiral model on the half-line, and rational solutions of the boundary Yang-Baxter equation (BYBE). In each case we find a connection with (type I, Riemannian, globally) symmetric spaces G/H: there is a class of integrable BCs in which the boundary field is restricted to lie in a coset of H; these BCs are parametrized by G/H×G/H; there are rational solutions of the BYBE in the defining representations of all classical G parametrized by G/H; and using these we propose boundary S-matrices for the principal chiral model, parametrized by G/H×G/H, which correspond to our boundary conditions.

U2 - 10.1007/s00220-002-0735-y

DO - 10.1007/s00220-002-0735-y

M3 - Article

SN - 0010-3616

VL - 233

SP - 313

EP - 354

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -